Formulas

Question 1

Distance, Rate, Time

Answer 1

D = R × T

Question 2

Core Arithmetic

Answer 2

Percent, Ratio, and Average formulas

Question 3

Basic Geometry Area

Answer 3

Triangle, Rectangle, and Circle area formulas

Question 4

Right Triangles

Answer 4

Pythagorean theorem (a² + b² = c²)

Question 5

Algebra Foundations

Answer 5

Slope, Line, and Exponent rules

Question 6

Quadratics

Answer 6

Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a

Question 7

Percent (Tip: Always think “out of 100.”)

Answer 7

% = (part ÷ whole) × 100

Question 8

Finding part (Ex: 20% of 60 = 12)

Answer 8

part = % × whole

Question 9

Percent change (Tip: Watch for increase vs. decrease)

Answer 9

((new - old) / old) * 100

Question 10

Ratio (Tip: Simplify to lowest terms)

Answer 10

a : b = a ÷ b

Question 11

Average (Tip: Used in many word problems)

Answer 11

sum / number of terms

Question 12

Distance

Answer 12

D = R × T

Question 13

Work (Tip: “Together” problems)

Answer 13

(Rate1 + Rate2) * Time = Work

Question 14

Mixture (Tip: Used for combining percentages)

Answer 14

(Amt1×Conc1 + Amt2×Conc2) / total amt

Question 15

Slope (Tip: Rise over run)

Answer 15

m = (y2 - y1) / (x2 - x1)

Question 16

Point-slope form (Tip: Handy for line equations)

Answer 16

y - y1 = m(x - x1)

Question 17

Slope-intercept form (Tip: m = slope, b = y-intercept)

Answer 17

y = mx + b

Question 18

Quadratic formula (Tip: Memorize pattern)

Answer 18

x = [-b ± √(b² - 4ac)] / 2a

Question 19

Exponents (Tip: Same base = add/subtract)

Answer 19

a^m * a^n = a^(m+n)

Question 20

Power of power (Tip: Multiply exponents)

Answer 20

(a^m)^n = a^(m*n)

Question 21

Negative exponent (Tip: Flip it)

Answer 21

a^-n = 1 / a^n

Question 22

Distributive property

Answer 22

a(b + c) = ab + ac

Question 23

Factoring (Tip: m*n=c, m+n=b)

Answer 23

x² + bx + c = (x + m)(x + n)

Question 24

Rectangle area

Answer 24

A = l * w

Question 25

Triangle area

Answer 25

A = 1/2 b * h

Question 26

Circle area

Answer 26

A = πr²

Question 27

Circle circumference

Answer 27

C = 2πr or πd

Question 28

Trapezoid area

Answer 28

A = 1/2 (b1 + b2) * h

Question 29

Pythagorean theorem (Notes: Right triangles)

Answer 29

a² + b² = c²

Question 30

Distance formula (Notes: Coordinate geometry)

Answer 30

√[(x2 - x1)² + (y2 - y1)²]

Question 31

Midpoint formula

Answer 31

((x1 + x2)/2 , (y1 + y2)/2)

Question 32

Probability (Ex: P(odd on die) = 1/2)

Answer 32

P = favorable / total

Question 33

Complement rule

Answer 33

P(not A) = 1 - P(A)

Question 34

Combinations (Tip: Rare)

Answer 34

nCr = n! / [r!(n - r)!]

Question 35

Median

Answer 35

Middle number in sorted list

Question 36

Mode

Answer 36

Most frequent number in set